Hydrogen exists in its atomic state throughout interstellar space, on the order of about one hydrogen atom per cubic meter of space. Hydrogen exists across Earth in the form of chemical compounds like carbohydrates, hydrocarbons, hydrogen halides, metal hydrides, and even comprises about 0.00005% by volume of the Earth's atmosphere. Considering the vast size of the Earth's atmosphere, even this small percentage represents a large amount of hydrogen gas. And finally, the most abundant hydrogen-containing chemical compound found on Earth is water. Water covers about 70% of the surface of the Earth, which indicates that there is plenty of hydrogen available from which to produce hydrogen gas (H2). The challenge is figuring out how to extract the hydrogen from its known sources in an environmentally beneficial and energy economical manner.
Hydrogen containing compounds fall into two groups: 1) hydrogen bearing and 2) hydrogen and energy bearing. Water belongs in the first group. Compounds, such as methane, belong in the second group.
Methane will react with steam over a nickel catalyst at 1200° K and one atmosphere to produce hydrogen as follows:CH4 (g)+H2O (v)→CO (g)+3H2 (g)  (1)
This is a spontaneous reaction with a ΔG=−77.7 kJ/mole CH4.
When a spontaneous chemical reaction occurs, the decrease in free energy, −ΔG, corresponds to the maximum amount of useful work, Wmax, which can be obtained from the reaction:−ΔG=Wmax  (2)
For a chemical reaction which is not spontaneous, ΔG is positive and Wmax is negative. What this means is that work must be done on the system through an external source of energy to cause the reaction to occur. The minimum amount of work that must be done on the system is given by ΔG.
Water will theoretically react with four electrons influenced by an electric potential of 1.23 volts (V) to produce hydrogen as follows:2H2O (l)O2 (g)+4H+ (aq)+4e−  (3)4H+ (aq)+4e−2H2 (g)  (4)Net: 2H2O (l)O2 (g)+2H2 (g) ΔH=−48.5 kJ/mole H2  (5)
This is an exothermic reaction.
However, the theoretical 1.23 V is not achieved in commercial-scale electrolysis. In commercial scale electrolysis, water will react with four electrons influenced by an electric potential of ˜1.75 V to produce hydrogen as follows:Net: 2H2O (l)O2 (g)+2H2 (g) ΔH=+51.8 kJ/mole H2  (6)
Unlike the theoretical reaction (5), this is an endothermic reaction, and thus requires the input of energy for the reaction to be initiated and run.
The enthalpy of reaction (ΔH) for the theoretical reaction of water with four electrons at 1.23 V, described by equation (5), is a combination of the energy terms for both the forward electrolysis reaction and the reverse recombination reaction, the difference between the energy of formation for hydrogen from water (237.4 kJ/mole H2 @ 1.23 V) and the heat of formation (ΔHf) of water (285.9 kJ/mole H2O) (i.e., heat of combustion of one mole of H2) or:237.4 kJ/mole−285.9 kJ/mole=−48.5 kJ/mole H2  (7)
Because electrolysis in the real world does not operate at the theoretical minimum potential of 1.23 V, but instead operates at ˜1.75 V, we are forced to work with the endothermic reaction found in equation (6) instead of the exothermic reaction found in equation (5).
The forward electrolysis reaction described by equation (5) moves through a theoretical potential of 1.23 volts and yields the specific energy of formation for hydrogen found in equation (7):(4e−/2 molecules H2)×(1.6022×10−19 C/e−)×(1.23 J/C)=3.9414×10−19 J/molecule H2  (8)(3.9414×10−19 J/molecule H2)×(6.0221×1023 molecules/mole)=237.4 kJ/mole H2  (9)
The heat of formation (ΔHf) for one mole of water is:ΔHf of H2O (liquid)=285.9 kJ/mole H2O  (10)
Since there is one mole of H2 for every mole of H2O:ΔH combustion of H2 (g)=285.9 kJ/mole H2  (11)
The enthalpy of reaction for the actual reaction of water with four electrons at 1.75 V, described by equation (6), is a combination of the energy terms for both the forward electrolysis reaction and the reverse recombination reaction:337.7 kJ/mole (@1.75 V)−285.9 kJ/mole=+51.8 kJ/mole H2  (12)
The forward electrolysis reaction described by equation (6) moves through an actual potential of 1.75 volts and yields the specific energy of formation for hydrogen found in equation (12):(4e−/2 molecules H2)×(1.6022×10−19 C/e−)×(1.75 J/C)=5.6077×10−19 J/molecule H2  (13)(5.6077×10−19 J/molecule H2)×(6.0221×1023 molecules/mole)=337.7 kJ/mole H2  (14)
Because commercial-scale electrolysis of water takes place at ˜1.75 V, instead of the theoretical minimum potential of 1.23 V, the maximum system energy recovery from electrolysis achieved through the reverse recombination reaction found in equation (6) is:(285.9 kJ/mole)/(337.7 kJ/mole)×100%=84.7%  (15)
Hydrogen-powered fuel cells operate at 1.23 V of electrical potential. Therefore, the maximum system energy recovery that could be achieved by running a fuel cell from the hydrogen gas generated by the 1.75 V potential forward electrolysis reaction found in equation (6) is:(237.4 kJ/mole)/(337.7 kJ/mole)×100%=70.3%,  (16)
which is the ratio of 1.23 volts to 1.75 volts times 100%.
From an energy economical standpoint, equation (1) would be the more favorable route for producing hydrogen gas. However, there is a limited supply of methane and the oxidation of the carbon monoxide produces carbon dioxide, which is a greenhouse gas. From an environmentally beneficial standpoint, equation (6) would be the more favorable route for producing hydrogen. However, this route requires an external source of clean energy to maintain its environmental benefit.
The energy recovery of a system that combusts the hydrogen produced from the forward electrolysis reaction in equation (6) is 84.7%, as illustrated by equation (15). The energy recovery of a system that runs a fuel cell from the hydrogen produced from the forward electrolysis reaction in equation (6) is 70.3%, as illustrated by equation (16). These are two pathways that demonstrate that water is in fact a hydrogen carrier as opposed to a material like methane which is both a hydrogen and energy carrier. Therefore, the only way to increase the efficiency of converting electrical energy into hydrogen from water is to find a spontaneous or exothermic chemical reaction that could take place in the electrolysis cell and would couple the excess energy with the impressed voltage to lead to low splitting voltages—i.e., less than 1.23 volts.